Orbital Map

The orbital map places the solar system planets at their real position for any date between 1957 and 2060. Positions are computed from the approximate Keplerian elements of the planets published by JPL (NASA): an educational approximation, good enough to see where Earth and Mars are, how long light takes to cross between them and when they line up.

How trajectories are computed (Lambert’s problem)

Given a mission’s launch and arrival dates, the trajectory is the orbit around the Sun that joins Earth’s position on departure day with Mars’s on arrival day. Finding it is Lambert’s problem: two points, a flight time and the Sun’s gravity determine a single orbit (the short way round). Here it is solved with universal variables and returns the departure velocity; from it comes the C3 parameter (characteristic energy, in km²/s²), which measures how demanding the launch is. The lower the C3, the cheaper the mission.

Launch windows to Mars

Earth and Mars are in a favourable position for travelling between them about every 26 months (780 days), shortly before each opposition, when Earth overtakes Mars. Those are the launch windows. The table lists, for each window from 1957 to 2060, when it opens and closes (the days when leaving costs only a little more energy than at the best moment: at most 30% or 3 km²/s²), the minimum-energy departure date computed by the map, the matching arrival, the trip duration, the C3 and the nearest opposition. Values are indicative, not mission planning.

Signal delay

Radio signals travel at the speed of light (299,792 km/s). Since the Earth–Mars distance varies from about 55 million km (at the most favourable oppositions) to about 400 million, the one-way delay ranges from roughly 3 to 22 minutes. When Mars is on the far side of the Sun (solar conjunction) communications are interrupted for a while.